1. Field of the Invention
The invention pertains to the field of Doppler navigation systems and more particularly to the compensation for terrain bias errors in the Doppler frequency spectrum of such systems.
2. Description of the Prior Art
A Doppler navigation system, on a moving vehicle, employs a device to transmit signals, such as electromagnetic signals or acoustic signals, towards a surface (terrain). These signals are scattered from the terrain, with portions of the scattered signals being retrodirected (backscattered). Due to the motion of the vehicle, the frequency of the backscattered signals received at the vehicle undergo a Doppler frequency shift. The navigation system detects and utilizes this Doppler frequency to determine the velocity components of the vehicle. The Doppler frequency is related to the velocity of the vehicle by the basic equation f.sub.D =(2V cos .phi.)/.lambda., where f.sub.D is the Doppler frequency shift, V is the vehicle's velocity, .phi. is the angle between the velocity vector and the direction of signal propagation, and .lambda. is the wavelength of the transmitted signal.
Since the signal beam has a finite width, as shown in FIG. 1, and the signal return from the terrain is backscattered in a random like manner, the Doppler frequency within the beam is not a single frequency, but is a noiselike frequency spectrum, such as the spectrum 11 shown in FIG. 2. The central frequency of the frequency band between the 3 dB points of the spectrum is generally utilized in the above given equation to determine the velocity. The frequency bandwidth is dependent on the system beamwidth and may be expressed mathematically by .DELTA.f.sub.D =[(2V/.lambda.) sin .phi.] .DELTA..phi., where .DELTA.f.sub.D is the half power spectrum bandwidth, and .DELTA..phi. is the two-way system beamwidth.
If the scattering terrain were shaped in a manner to be equal distant from the transmitting device for all rays within the 3 dB beamwidth, as shown by the arc 13 in FIG. 1, the central frequency f.sub.D =(2V cos .phi..sub.0)/.lambda. of the spectrum 11 would be the Doppler shift of the central ray 15 in two way system pattern, where .phi..sub.0 is the angle from the velocity vector of the central ray 15. Slant ranges within the 3 dB points of the two way system pattern, however, vary from r.sub.1 =h/sin (.phi..sub.0 -.DELTA..phi./2) to r.sub.2 =h/sin (.phi..sub.0 +.DELTA..phi./2), for typically flat horizontal terrain, and the amplitudes of the Doppler frequency signals vary in an inverse relationship to the slant range. With these variations the Doppler frequency spectrum will be skewed. This skewing causes the centroid of the Doppler spectrum to be shifted by .DELTA.f.sub.d,as shown by the spectrum 12 in FIG. 2, from the frequency f.sub.d at the central ray .phi..sub.0 of the two way system beamwidth. Since h, .phi..sub.0, and .DELTA..phi. are known, compensation for errors due to the range variations over the beamwidth may be made, provided that, within the two way beamwidth, the backscatter coefficient over the illuminated terrain is relatively constant and not a function of the incident ray angle.
The amplitude M(.phi.) of the Doppler signal at each angle within the beam is generally proportional to G(.phi.), R(.phi.), and A(.phi.); where G(.phi.) is the value of the two way beam pattern at the angle .phi., R(.phi.) is the backscatter coefficient of the terrain at the angle of incidence corresponding to the beam angle .phi., and A(.phi.) is the slant range attenuation at the beam angle .phi.. Consequently, the amplitude of the Doppler frequency spectrum will not, in general, be symmetrical, but would be skewed, as shown by the spectrum 12 of FIG. 2. Generally, terrain backscatter coefficient variations within the beamwidth are not known. As a result, compensation for these variations can not be accurately applied. Under normal conditions the variation of the terrain's backscatter coefficient with the incident angle is the primary cause of the residual velocity error of a precision Doppler navigation system.
The above discussion relates to the fundamental method of determining velocity with the measurement of the Doppler frequency shift experienced by backscattered signals received within a Doppler navigation system beamwidth. Since the velocity of a vehicle has three components, a minimum of three beams are required to determine the velocity vector. A Three beam system, comprising beams A1, A2, and A3 is shown in FIG. 3A and a four beam system, comprising beams B1, B2, B3, and B4 is shown in FIG. 3B. The four beam system is generally utilized. She four beam configuration, in addition to providing the velocity vector, minimizes the effects of the vehicle's roll and pitch on the detected Doppler frequency. The beams are symmetrically positioned about the vehicle's vertical axis 19 and the Doppler frequencies f.sub.D1 -f.sub.D4 at the centers of beams B1-B4, respectively, for this configuration are given by: EQU f.sub.D1 =2/.lambda.(-V.sub.H cos .alpha. cos .theta.+V.sub.D cos .alpha. sin .theta.+V.sub.V sin .alpha.) EQU f.sub.D2 =2/.lambda.(V.sub.H cos .alpha. cos .theta.+V.sub.D cos .alpha. sin .theta.+V.sub.V sin .alpha.) EQU f.sub.D3 =2/.lambda.(V.sub.H cos .alpha. cos .theta.-V.sub.D cos .alpha. sin .theta.+V.sub.V sin .alpha.) EQU f.sub.D4 =2/.lambda.(-V.sub.H cos .alpha. cos .theta.-V.sub.D cos .alpha. sin .theta.+V.sub.V sin .alpha.)
where:
V.sub.H is the heading velocity PA1 V.sub.D is the drift velocity PA1 V.sub.V is the vertical velocity PA1 .theta. is the angle between the beam centroid and the longitudinal axis of the vehicle
.alpha.is the angle between the beam centroid and the plane perpendicular to the vertical axis of the vehicle.
It should be evident from these equations that the heading velocity V.sub.H may be obtained from the average of the differences f.sub.D2 -f.sub.D1 and f.sub.D3 -f.sub.D4 ; V.sub.D may be obtained from the average of the differences f.sub.D1 -f.sub.D4 and f.sub.D2 -f.sub.D3 ; and V.sub.V may be obtained from the average f.sub.D1 +f.sub.D3 and f.sub.D2 +f.sub.D4.
Each of the beams B1-B4 is subject to the biases previously discussed. These biases, if not corrected, cause errors in the determination of the three velocity components, which in turn cause errors in the determination of the vehicle position.